We investigate smooth representations of complete Kac-Moody groups. We
approach representation theory via geometry, in particular, the group action on
the Davis realisation of its Bruhat-Tits building. Our results include an
estimate on projective dimension, localisation theorem, unimodularity and
homological duality.Comment: 28 pages. Version 3: some minor corrections, actions on simplicial
sets are explained. Version 4: minor correction
